Benabbas, Siavosh

Georgiou, Konstantinos

Abstract [en]

Recently, Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the MAX BISECTION problem. We improve their algorithm to a 0.8776-approximation. As MAX BISECTION is hard to approximate within alpha(GW) + epsilon approximate to 0.8786 under the Unique Games Conjecture (UGC), our algorithm is nearly optimal. We conjecture that MAX BISECTION is approximable within alpha(GW) - epsilon, that is, that the bisection constraint (essentially) does not make MAX CUT harder. We also obtain an optimal algorithm (assuming the UGC) for the analogous variant of MAX 2-SAT. Our approximation ratio for this problem exactly matches the optimal approximation ratio for MAX 2-SAT, that is, alpha(LLZ) + epsilon approximate to 0.9401, showing that the bisection constraint does not make MAX 2-SAT harder. This improves on a 0.93-approximation for this problem from Raghavendra and Tan.